Asymptotics for helmholtz and maxwell solutions in 3-D open waveguides

We extend classic Sommerfeld and Silver-Müller radiation conditions for bounded scatterers to acoustic and electromagnetic fields propagating over three isotropic homogeneous layers in three dimensions. If x= (x ₁,x₂,x₃) ∈ℝ³, with x ₃ denoting the direction orthogonal to the layers, standard conditions only hold for the outer layers in the region |x₃| > ||x||^γ, for γ∈ (1/4,1/2) and x large. For |x ₃| ≤ ||x||^γ and inside the slab, asymptotic behavior depends on the presence of surface or guided modes given by the discrete spectrum of the associated operator.